2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77848For an arrangement with complement X and fundamental group G, we relate the truncated cohomology ring, H^{<=2}(X), to the second nilpotent quotient, G/G_3. We define invariants of G/G_3 by counting normal subgroups of a fixed prime index p, according to their abelianization. We show how to compute this distribution from the resonance varieties of the Orlik-Solomon algebra mod p. As an application, we establish the cohomology classification of 2-arrangements of n<=6 planes in R^4.LaTeX2e, 22 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure MathematicsGeometric TopologyAlgebraic Geometry52B30, 57M05 (Primary); 20F14, 20J05 (Secondary)text